CircleDance | Topcoder Archive

Problem Statement

Given a group of dancers' heights, arrange a circle formation that minimizes the maximum height difference between each pair of neighboring dancers. Write a class CircleDance with a method arrangeDancers that takes a int[], heights, and returns the maximum height difference between neighboring dancers.

Definition

Class:: CircleDance
Method:: arrangeDancers
Parameters:: int[]
Returns:: int
Method signature:: int arrangeDancers(int[] heights)
(be sure your method is public)

Constraints

heights will contain between 3 and 20 elements inclusive.
Each element of heights will be between 150 and 210 inclusive.

Examples

```
{180,183,178,185}
```
```
Returns: 5
```
The dancers may be arranged in a circle like this: 180 / \ 185 178 \ / 183 Their height differences are shown below: 180 (5)/ \(2) 185 178 (2)\ /(5) 183 The maximum difference is 5. Other arrangements may not lead to an optimal solution. For example, the following one has a maximum difference of 7: 180 (3)/ \(2) 183 178 (2)\ /(7) 185
```
{170,180,190}
```
```
Returns: 20
```
Any arrangement is equivalent to the following one: 180 (10)/ \(10) 170 - 190 (20) So the result is 20.
```
{180,180,180,180,180}
```
```
Returns: 0
```

{184,165,175,186,192,200,176,192,194,168,205,201}

Returns: 10

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